IIM Indore - Indian Institute of Management

Placements: http://www.iimidr.ac.in/placements/
Faculty: http://www.iimidr.ac.in/faculty/

For BBA+MBA visit : http://www.iimidr.ac.in/academic-programmes/five-year-integrated-programme-in-management-ipm/ipm-admissions-details/.
For MBA(PGDM) visit : http://www.time4education.com/CAT-MBA/Admission-Criteria/IIM-Admission-Criteria.

Yes, there are many other institutions that provide the integrated management courses in India.
Eg: IIT Kharagpur, Vinod Gupta School Of Management, NMIMS, etc.

MBA(BBA+MBA) from IIM, Indore is a full-time course. For more details, please contact the college.
Email: ipmadmissions@iimidr.ac.in
Website: www.iimidr.ac.in

Candidates satisfying the following criteria are eligible to apply for the Five-Year integrated programme in management of IIM Indore.
General and NC-OBC Category:
Minimum 60% in standard X/ SSC and standard XII/HSC or equivalent examinations, maximum 20 years of age as on July 31, 2017.
SC, ST and PWD (DA) Category: minimum 55% in standard X/ SSC and standard XII/ HSC or equivalent examinations, maximum 22 years of age as on July 31, 2017

Questions might be on the resume, under graduation subjects, current affairs, specialization (if anything specific) into MBA, work experience, hobbies, extracurricular activities, achievements, leadership activities, internship experience, any projects (Live or academics).
Some of the general questions like:-
1. Tell me about yourself?
2. Why MBA?
3. Strengths and Weakness?
4. Biggest Achievement and Biggest Failure in Life till now?
5. What do you think about (any hot topic in current affairs)?
6. Long-term and short goals?

Please find the complete details on: http://www.iimidr.ac.in/academic-programmes/five-year-integrated-programme-in-management-ipm/ipm-admissions-details/.

Most probably yes. If the number of candidates who fall into this criteria is more, then shortlist depends on few other parameters which can be seen through the below link.
http://www.time4education.com/CAT-MBA/Admission-Criteria/IIM-Admission-Criteria.

IPMAT Age Criteria: (As per IPMAT 2018)
General and NC-OBC: Candidates should not be more than 20 years old as on Thursday, July 31, 2018.
SC, ST and PWD/DA Category: Candidates should not be more than 22 years old as on July 31, 2018.

Cutoff score differs every year and it will not be released officially. But one can get projected cutoff online. It will also differ based on the category of the candidate.
The pattern of AT-2017 is as follows:
AT will be of objective-type nature. The sample questions from previous year question paper will be uploaded on the website of IIM Indore (iimidr.ac.in). There will be two sections in AT namely quantitative ability and verbal ability.
There will be 100 questions in total with time duration of two hours.
Each question will carry 4 marks. There will be a negative marking of 1 mark for each wrong answer.